You might consider setting your problem up as a GLM/GAM. These use splines to to create a spatially smooth conditional mean surface. You can find examples of this in:
Waller and Gotway. "Applied Spatial Statistics for Public Health Data"
and
Wood. "Generalized Additive Models: An introduction with R"
The latter also serves as a comprehensive guide to the mgcv package.
However, since these create smooth surfaces (and if you do not have spatially discontinuous covariate effects, you didn't mention this), I wouldn't expect the exact results to be that different from those obtained at the nearest raster cell.
Good luck,
Nicholas
Nicholas N. Nagle, Assistant Professor
University of Colorado
Department of Geography
UCB 260, Guggenheim 110
Boulder, CO 80309-0260
phone: 303-492-4794